The present invention relates to a new and distinct sport of Sedum ellacombianum plant named ‘Cutting Edge’ characterized by yellow edged foliage all growing season long, compared to the all green foliage of the parent plant. The new Sedum ellacombianum was found as a naturally occurring, whole plant sport of an unnamed Sedum ellacombianum, not patented, in Hebron, Ill. in 2013. The selection of the new plant was due to its' yellow edged foliage, compared to the green foliage of the parent plant. Initial asexual reproduction has taken place at a nursery in Hebron, Ill. since 2014 by means of division, and vegetative cuttings. The new Sedum ellacombianum has shown to be stable and identical in reproduction after rooting over 1000 plants from 2014 to 2015. No plants of the new Sedum ellacombianum have been sold in this country, or anywhere in the world, prior to the filing of this application, nor has any disclosure of the new plant been made prior to the filing of this application with the exception of that which was disclosed within one year of filing of this application and was either derived directly or indirectly for the inventor.